Question

question 6
a cone is a solid with base that is a ______, a point not in the same plane as the base, and all the points between them.
a. rectangle
b. triangle
c. square
d. disc

question 7
which of the following has two congruent parallel discs for bases?
a. cylinder
b. prism
c. cone
d. pyramid

question 10
what is the surface area of the right prism given below?
a. $1200$ units$^2$
b. $350$ units$^2$
c. $600$ units$^2$
d. $520$ units$^2$

question 11
what is the surface area of the regular pyramid given below?
a. $189$ units$^2$
b. $140$ units$^2$
c. $280$ units$^2$
d. $329$ units$^2$

Explanation:

Question 6

Step1: Recall cone base definition

A cone's base is a circular flat surface, which is a disc.

Question 7

Step1: Recall 3D solid base properties

A cylinder has two congruent parallel circular discs as bases.

Question 10

Step1: Calculate base area

The base is a right triangle. Area: $\frac{1}{2} \times 8 \times 15 = 60$

Step2: Calculate lateral face areas

First, find hypotenuse of base: $\sqrt{8^2 + 15^2} = 17$
Lateral areas: $8 \times 10 = 80$, $15 \times 10 = 150$, $17 \times 10 = 170$

Step3: Total surface area

Sum 2 bases + lateral areas: $2 \times 60 + 80 + 150 + 170 = 600$

Question 11

Step1: Calculate base area

Base is a square: $7 \times 7 = 49$

Step2: Calculate slant height (missing)

Assuming slant height $l$: each triangular face area $\frac{1}{2} \times 7 \times l$. Total lateral area $4 \times \frac{1}{2} \times 7 \times l = 14l$

Step3: Match total surface area

Total area = $49 + 14l$. Testing options: $49 + 14l = 189 \implies 14l=140 \implies l=10$ (valid slant height)

Answer:

Question 6: D. disc
Question 7: A. Cylinder
Question 10: C. $600$ units$^2$
Question 11: A. $189$ units$^2$